This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A018922 #29 Sep 21 2024 13:29:06
%S A018922 8,16,31,60,116,224,432,833,1606,3096,5968,11504,22175,42744,82392,
%T A018922 158816,306128,590081,1137418,2192444,4226072,8146016,15701951,
%U A018922 30266484,58340524,112454976,216763936,417825921,805385358,1552430192,2992405408,5768046880
%N A018922 Define the generalized Pisot sequence T(a(0),a(1)) by: a(n+2) is the greatest integer such that a(n+2)/a(n+1) < a(n+1)/a(n). This is T(8,16).
%C A018922 Not to be confused with the Pisot T(8,16), which is essentially A000079. - _R. J. Mathar_, Feb 13 2016
%H A018922 Colin Barker, <a href="/A018922/b018922.txt">Table of n, a(n) for n = 0..1000</a>
%H A018922 D. W. Boyd, <a href="http://www.researchgate.net/publication/258834801">Linear recurrence relations for some generalized Pisot sequences</a>, Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993.
%H A018922 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,0,0,-1).
%H A018922 <a href="/index/Ph#Pisot">Index entries for Pisot sequences</a>
%F A018922 a(n) = 2*a(n-1) - a(n-5).
%F A018922 a(n) = A107066(n+3). - _Vladimir Joseph Stephan Orlovsky_, Jul 08 2011
%F A018922 O.g.f: -(-8+x^2+2*x^3+4*x^4)/((x-1)*(x^4+x^3+x^2+x-1)) = (1/3)/(x-1)+(1/3)*(-13*x^3-20*x^2-24*x-25)/(x^4+x^3+x^2+x-1) . - _R. J. Mathar_, Dec 02 2007
%t A018922 Drop[CoefficientList[Series[1/(1 - 2*z + z^5), {z, 0, 100}], z], 3] (* _Vladimir Joseph Stephan Orlovsky_, Jul 08 2011 *)
%t A018922 RecurrenceTable[{a[1] == 8, a[2] == 16, a[n] == Ceiling[a[n-1]^2/a[n-2]] - 1}, a, {n, 40}] (* _Bruno Berselli_, Feb 17 2016 *)
%t A018922 LinearRecurrence[{2,0,0,0,-1},{8,16,31,60,116},40] (* _Harvey P. Dale_, Sep 21 2024 *)
%o A018922 (PARI) T(a0, a1, maxn) = a=vector(maxn); a[1]=a0; a[2]=a1; for(n=3, maxn, a[n]=ceil(a[n-1]^2/a[n-2])-1); a
%o A018922 T(8, 16, 40) \\ _Colin Barker_, Feb 14 2016
%o A018922 (Magma) Tiv:=[8,16]; [n le 2 select Tiv[n] else Ceiling(Self(n-1)^2/Self(n-2))-1: n in [1..40]]; // _Bruno Berselli_, Feb 17 2016
%Y A018922 Cf. A107066.
%K A018922 nonn,easy
%O A018922 0,1
%A A018922 _R. K. Guy_